Level Tapering

Let’s start with level tapering, considering a basic arena shape in the vertical plane: longest throw to the top – shortest to the bottom. Is the relationship of level taper to line breaking a digital phenomenon? (i.e., 1 or 0? Broken or unbroken?)

It’s assured that our line is unbroken if we have a line of 16 identical boxes at the same level. If one box is turned down 0.1 dB, is the line broken or just slightly bent? If you think it’s broken already, here’s some bad news: You’ve never heard an unbroken line because manufacturing tolerances aren’t that good. How about variations of 1 dB? Again, nobody can deliver 16 boxes that are within a single dB.

Let’s step it up: Turn the bottom box down 6 dB. This makes it effectively half a box. The loss in the lowest frequency range (where directionality is so low and wavelengths so large that they sum well) that the combined response is reduced by less than 0.25 dB. This does not seem so scary in the big picture, does it?

Let’s go further and reduce 3 boxes by 6 dB. The lowest frequencies now lose 1 dB. The high frequencies, meanwhile, are substantially reduced in the area where the bottom three boxes are pointed – such as the early rows of seats. This is a tangible benefit (up to 6 dB of HF control) for a minimal cost (1 dB loss in overall LF power). Is the line broken now? If so, how can I tell? Is it broken everywhere or just at one place? Is it broken at all frequencies?

It should be easy to find the break point at 10 kHz, since there’s enough directional control to hear the isolated areas on either side of our fault line. You could find it blind-folded or measure it with an analyzer. Do you think you can identify a break point at 100 Hz? Good luck. These large wavelengths don’t turn on a dime. When people talk fretfully of breaking the line is it the VHF range they are worried about? Not from what I hear. The concerns I hear are much more about the lows than the highs.

A practical taper should be more gradual, with 1-3 dB steps being more typical – and which makes it difficult to locate the transitions in the space. If we tapered the bottom 5 boxes at 3-3-3-6-6 dB, we would get an overall LF loss of 1 dB and gain substantial HF steering. The same price would be paid for a taper of 1-1-1-1-2-2-4-4 dB on the bottom 8 boxes of a 16-element array. These are just two of a myriad of options that can be employed to help tailor the response of our bent/broken system to the shape of the audience.

The trade-off for the potential problems this tapering might cause also includes additional benefits: besides increasing front-back level uniformity in the HF range, it also improves uniformity (to a lesser extent) as frequency falls – all the way down. The dB that we lose in the low end is offset by the fact that the beam center is steered upward off the floor and therefore spread more evenly front to back.